How fast does a plane have to go to reach the heat barrier?

It depends on geometry, material of construction surface roughness and altitude.

Practically speaking this problem is designed around. The Concorde would routinely fly across the Atlantic at Mach 2 at 50,000 ft where the air is thin enough to reduce frictional heating. The SR71 (Blackbird) could handle Mach 3 by flying even higher and designing the plane so it could literally expand (Of course, when cool on the ground, it was so loose the fluids leaked out of it). The space shuttles use ablative tiles to protect against the heat of reentry.

So you can see the answer is "it depends"

Just about all re-entering space junk and vehicle is subjected to heat barrier phenomenon, but plains flying low and long distance (time element) get warm too over the period of flight due to friction from air resistant.

So it is dependent on many factors. I believe re -entry speeds can be any where between 46K to 27K miles /hour.

Most plains fly at an altitude betwee 27 K to 40 K feet. The outside temperature can be around -37 degrees F or colder, which helps cool the plain. The direct non-stop flight between New York USA and Bombay India is about 16 hours.

Most large plains use computer to find jet stream, and take advantage of the winds within the jet stream to reduce the fuel consumption.